A RKHS bound for \(L_{K,X}(f)-L_K(f)\)  has been available in [1]}, [2]} based on an integral operator approach. However, such an analysis usually requires the response \(Y\)  to be uniformly bounded, which excludes nonparametric regression that assumes Gaussian error. [3]} adopted the operator-theoretic approach and extended it to unbounded sampling process and general Mercer kernels, which provided the following non-asymptotic RKHS bound for \(\hat{f}_n - f_{\lambda }\)  using Hanson-Wright inequality [4]} and equivalent kernels. For ease of reference we provide it below; see Theorem 1 in [3]} for a proof.
